Kärkkäinen, Salme Orientation analysis of stochastic fibre systems with an application to paper research. (English) Zbl 1026.62102 Report. University of Jyväskylä. Department of Mathematics and Statistics. 89. Jyväskylä: Univ. of Jyväskylä, Dept. of Mathematics and Statistics, 53 p. (2003). This thesis deals with statistical analysis of orientation distribution for stochastic systems of fibres (thickened curves or segments). The problem is motivated by the analysis of paper microstructure. The author assumes that the observed fibres are described as long and narrow sets around central fibres being lined segments. The objective is to estimate the orientation distribution of the central fibres from observations of the system of overlapping thickened fibres. The situation is even more complicated if one observes a grey-scale image of a fibre system, where it is extremely difficult to isolate individual fibres.The basic idea of the suggested method is a relationship between the scaled variogram of the random field representing the grey-scale image and the intensity of the central fibres. Then a parametric method for the orientation distribution can be fitted by least-squares type procedures. The new methods have been used to analyse empirical data from paper technology research.The thesis comprises a preprint and the following three papers co-authored by the dissertant: Adv. Appl. Probab. 33, 559-575 (2001; Zbl 0986.62073)]; Image Anal. Stereol. 20, 199-202 (2001; Zbl 0986.62109); J. Microscopy 207, 69-77 (2002). Reviewer: I.S.Molchanov (Glasgow) MSC: 62M40 Random fields; image analysis 60K99 Special processes 62P30 Applications of statistics in engineering and industry; control charts 60D05 Geometric probability and stochastic geometry Keywords:fibre process; orientation distribution; paper technology Citations:Zbl 0986.62073; Zbl 0986.62109 PDFBibTeX XMLCite \textit{S. Kärkkäinen}, Orientation analysis of stochastic fibre systems with an application to paper research. Jyväskylä: Univ. of Jyväskylä, Dept. of Mathematics and Statistics (2003; Zbl 1026.62102)